Analytic Number Theory

doi:10.1017/CBO9780511666179

This volume presents an authoritative, up-to-date review of analytic number theory. It contains outstanding contributions from leading international figures in this field. Core topics discussed include the theory of zeta functions, spectral theory of automorphic forms, classical problems in additive number theory such as the Goldbach conjecture, and Diophantine approximations and equations. This will be a valuable book for graduates and researchers working in number theory.

‘ … a good overview over the recent state of art in this part of Number Theory.’

Source: Monatshefte für Mathematik

‘ … an authoritative, up-to-date review of analytic number theory. This will be a valuable book for graduates and researchers working in number theory.’

Source: L’Enseignement Mathématique

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Foreword
pp vii-viii
- By Yoichi Motohashi
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Speakers
pp ix-x
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1 - Subvarieties of Linear Tori and the Unit Equation A Survey
pp 1-20
- By Enrico Bombieri
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2 - Remarks on the Analytic Complexity of Zeta Functions
pp 21-30
- By Enrico Bombieri
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3 - Normal Distribution of Zeta Functions and Applications
pp 31-42
- By Enrico Bombieri, Alberto Perelli
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4 - Goldbach Numbers and Uniform Distribution
pp 43-52
- By Jörg Brüdern, Alberto Perelli
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5 - The Number of Algebraic Numbers of Given Degree Approximating a Given Algebraic Number
pp 53-84
- By Jan-Hendrik Evertse
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6 - The Brun–Titchmarsh Theorem
pp 85-94
- By John Friedlander, Henryk Iwaniec
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7 - A Decomposition of Riemann's Zeta-Function
pp 95-102
- By Andrew Granville
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8 - Multiplicative Properties of Consecutive Integers
pp 103-118
- By Adolf J. Hildebrand
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9 - On the Equation (xm – 1)/(x – 1) = yq with x Power
pp 119-126
- By Noriko Hirata-Kohno, Tarlok N. Shorey
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10 - Congruence Families of Exponential Sums
pp 127-138
- By Martin N. Huxley, Nigel Watt
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11 - On Some Results Concerning the Riemann Hypothesis
pp 139-168
- By Aleksandar Ivić
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12 - Mean Values of Dirichlet Series via Laplace Transforms
pp 169-208
- By Matti Jutila
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13 - The Mean Square of the Error Term in a Genelarization of the Dirichlet Divisor Problem
pp 209-226
- By Kai-Yam Lam, Kai-Yam Tsang
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14 - The Goldbach Problem with Primes in Arithmetic Progressions
pp 227-252
- By Ming-Chit Liu, Tao Zhan
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15 - On the Sum of Three Squares of Primes
pp 253-264
- By Hiroshi Mikawa
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16 - Trace Formula over the Hyperbolic Upper Half Space
pp 265-286
- By Yoichi Motohashi
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17 - Modular Forms and the Chebotarev Density Theorem II
pp 287-308
- By V. Kumar Murty
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18 - Congruences between Modular Forms
pp 309-320
- By M. Ram Murty
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19 - Regular Singularities in G-Function Theory
pp 321-336
- By Makoto Nagata
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20 - Spectral Theory and L-functions
pp 337-342
- By Peter Sarnak
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21 - Irrationality Criteria for Numbers of Mahler's Type
pp 343-352
- By Tarlok N. Shorey, Robert Tijdeman
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22 - Hypergeometric Functions and Irrationality Measures
pp 353-360
- By Carlo Viola
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23 - Forms in Many Variables
pp 361-376
- By Trevor D. Wooley
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24 - Remark on the Kuznetsov Trace Formula
pp 377-382
- By Eiji Yoshida
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Analytic Number Theory

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Foreword
pp vii-viii

Speakers
pp ix-x

1 - Subvarieties of Linear Tori and the Unit Equation A Survey
pp 1-20

2 - Remarks on the Analytic Complexity of Zeta Functions
pp 21-30

3 - Normal Distribution of Zeta Functions and Applications
pp 31-42

4 - Goldbach Numbers and Uniform Distribution
pp 43-52

5 - The Number of Algebraic Numbers of Given Degree Approximating a Given Algebraic Number
pp 53-84

6 - The Brun–Titchmarsh Theorem
pp 85-94

7 - A Decomposition of Riemann's Zeta-Function
pp 95-102

8 - Multiplicative Properties of Consecutive Integers
pp 103-118

9 - On the Equation (xm – 1)/(x – 1) = yq with x Power
pp 119-126

10 - Congruence Families of Exponential Sums
pp 127-138

11 - On Some Results Concerning the Riemann Hypothesis
pp 139-168

12 - Mean Values of Dirichlet Series via Laplace Transforms
pp 169-208

13 - The Mean Square of the Error Term in a Genelarization of the Dirichlet Divisor Problem
pp 209-226

14 - The Goldbach Problem with Primes in Arithmetic Progressions
pp 227-252

15 - On the Sum of Three Squares of Primes
pp 253-264

16 - Trace Formula over the Hyperbolic Upper Half Space
pp 265-286

17 - Modular Forms and the Chebotarev Density Theorem II
pp 287-308

18 - Congruences between Modular Forms
pp 309-320

19 - Regular Singularities in G-Function Theory
pp 321-336

20 - Spectral Theory and L-functions
pp 337-342

21 - Irrationality Criteria for Numbers of Mahler's Type
pp 343-352

22 - Hypergeometric Functions and Irrationality Measures
pp 353-360

23 - Forms in Many Variables
pp 361-376

24 - Remark on the Kuznetsov Trace Formula
pp 377-382

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Analytic Number Theory

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